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C13×D1309 #46801351

order34034
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D1309
unambiguous semidirect productC7⋊(C13×D187)
unambiguous semidirect productC11⋊(C13×D119)
unambiguous semidirect productC17⋊(C13×D77)

Splittings

Fitting, socle, HallC7×C11×C13×C17 ⋊ C2
derived, HallC7×C11×C17 ⋊ C2×C13
HallC11×C13×C17 ⋊ D7
HallC7×C13×C17 ⋊ D11
HallC7×C11×C13 ⋊ D17
HallC13×C17 ⋊ D77
HallC11×C17 ⋊ C13×D7
HallC11×C13 ⋊ D119
HallC7×C17 ⋊ C13×D11
HallC7×C13 ⋊ D187
HallC7×C11 ⋊ C13×D17
SylowC17 ⋊ C13×D77
SylowC11 ⋊ C13×D119
SylowC7 ⋊ C13×D187

Subgroups

subgroupG/H
center, hypercenterC13D1309
commutator, cosocle, hypocenterC7×C11×C17C2×C13
FrattiniC1G
Fitting, socleC7×C11×C13×C17C2
LCSG ▷ C7×C11×C17
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17017

Conjugacy classes & character table

8528 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34034, 14);